Mirrors, lenses, and other optical components are used in a variety of demanding applications ranging from space telescopes to laser systems. Such systems require optical components with very accurate surface configurations. Even slight deviations from the desired surface configuration can cause severe degradation in system performance, which may not be recognized until the system is deployed. A well known and unfortunately costly example of a lens system having unwanted deviations from the desired configuration is the Hubbell Space Telescope.
Currently, interferometers are used with optical test-sets to measure the surface of an optical element to fractions of a wavelength. A test-set generally includes the optical element being tested together with a holographic optical element (HOE) that has been designed to obtain a null wave front (i.e. no fringes, or very few fringes, in the interferogram obtained by testing with normal incidence light at the optical surface under test). Test-sets designed for testing large highly aspheric optics commonly contain a significant amount of optical distortion. Usually, a commercial interferometer is used with a test-set. Both the interferometer and the test-set can potentially contribute to the distortion. However, since commercial interferometer vendors do not provide the optical prescription of the interferometer for proprietary reasons, the optical distortion of the interferometer cannot be modeled. (As a rule of thumb, the steeper the optical element being tested, the more distortion that will be created since the HOE or lens must do more work by diffracting the rays to make them normal to the optical surface at all points).
Even a perfect optical system with a perfect test optical element can still have distortion. There are two forms of distortion that one may encounter with optical testing: optical distortion and geometric perspective distortion. Optical distortion occurs because the rays of light enter the HOE with one trajectory but leave the HOE with another. The HOE diffractively redirects the incident light so that it will be normal to the ideal optical surface under test, thus guaranteeing that the light will return on itself to the interferometer. The change in trajectory of the light after the HOE, or lens, distorts the image of the test optical element.
Geometric perspective distortion is typically created in the data processing when the data is intentionally transformed or distorted to convert to another geometric perspective. This is like transforming the X, Y, and Z coordinates of an object, commonly seen in image processing programs, to view the object from another angle. One case where a perspective change in the data is required is when the surface data is measured with the incident light normal to the surface everywhere but the polishing machine removes material in the Z-direction only (i.e. roughly normal to the flat back surface of the mirror) and does not have the capability to remove material normal to the optical surface. It is possible that the test-set will be responsible for contributing to the geometric distortion in cases where the test-optic is not being tested with normal incidence light, such as an elliptical or hyperbolic surface. The result of geometric distortion is that the image of the optical element being tested will look spatially distorted relative to the actual optical element. Failure to understand and correct for this distortion will result in a poor convergence of the testing and polishing cycles for the optical element. In the case of severe distortion, it is possible that the optical testing and polishing process will never converge and it will not be possible to complete the optical element to specification.
In order to understand and correct for the optical distortion of the test-set, present practice involves removing the optical element being tested from the test-set and applying an array of four paint spots (i.e. fiducial markings) onto the surface of the optical element using the metal probe of a coordinate measuring machine. The fiducials are placed in the form of a rectangle, a square, or a diamond, depending on the shape and orientation of the optical element. The fiducials are usually placed near the edge of the optical element. The coordinate measuring machine (CMM) uses a spring-loaded, ruby-tipped probe that is dipped in a 50/50 mixture of type correcting fluid (e.g. Whiteout.TM.) and water to place the temporary marks on the optical element. The optical element is then replaced in the test-set and the pattern of marks is observed at the interferometer. The observed surface data is distortion corrected using a nonlinear Cartesian or radial polynomial. The imaged fiducials that appear on the surface map are used to establish spatial correspondence between the data and its coordinate system before applying the distortion correction function.
Creating the distortion correction function is a logical and systematic procedure but involves several detailed steps. The location of the fiducials are determined by performing a linear transformation of the data onto the desired coordinate system. Linear transformations allow rotation, scaling, and offset (distortion is considered a nonlinear transformation). Although it is possible to correct the distortion of an image of the test optic with software based on the locations of the four fiducials, no unique conclusions can be made about the accuracy of the applied distortion correction. The imaged locations of the four fiducials do not provide enough information for visual feedback or enough information for a mathematical analysis. The raw surface data initially acquired by the interferometer must go through between 2 and 4 linear and nonlinear transformations before it is fully distortion corrected and ready to be used as hit-map to polish an optic. A hit-map is the term used for the final distortion corrected test-set data that is provided to a polishing machine (i.e. small tool polisher or ionfigure machine). The polishing machine then converts the XYZ data to specific machine instructions to control various parameters in the polishing process. The design and application of these transformations are complex and prone to error. A person looking at a distortion corrected image has no way to either visually or mathematically confirm the validity of these transformations based on the surface data or the 4 fiducials other that to say "yes, it looks like the data has been spatially warped".
This fiducial application process is time consuming and therefore costly, and the repeated handling of the optical element under test poses the risk of damaging a highly expensive optical element. There is a need therefore for an improved method and apparatus for testing an optical element that avoids the shortcomings of the prior art technique.